Contribution and Reservation

4·10²⁴⁵+1 =: 4(0)₂₄₄1_<246>; = 7 · 19 · 367885532726263369_<18> · [8175148325906903122680185625669425023660537155932173967065765979014371672879372506633237742369517012811587639114220441728682304334212857047154742376051912609932907164545250372048695079876661938736569839930275314631428703255013_<226>] SUBMIT/RESERVE

Status

Expression:	4·10²⁴⁵+1
Composite Factor:	817514832590690312268018562566942502366053715593217396706576 597901437167287937250663323774236951701281158763911422044172 868230433421285704715474237605191260993290716454525037204869 5079876661938736569839930275314631428703255013 (226-digit)
Status:	Not factored. Not reserved. You can submit its factors or reserve it for submitting in the future.

How to factor it

ECM, P-1, P+1

Look for prime factors by GMP-ECM first. Refer to the section "Efforts by ECM". Not only ECM but also P-1/P+1 may be helpful.

SNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 246.30-digit and the GNFS difficulty is 225.91-digit. SNFS must be faster than GNFS. It will take about 676 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 40001_245.
Put the following polynomial file 40001_245.poly in there too.
And then, run "perl factMsieve.pl 40001_245".

40001_245.poly ^*1

n: 8175148325906903122680185625669425023660537155932173967065765979014371672879372506633237742369517012811587639114220441728682304334212857047154742376051912609932907164545250372048695079876661938736569839930275314631428703255013
m: 100000000000000000000000000000000000000000
deg: 6
c6: 2
c0: 5
skew: 1.16
type: snfs
lss: 1
rlim: 89000000
alim: 89000000
lpbr: 30
lpba: 30
mfbr: 61
mfba: 61
rlambda: 2.7
alambda: 2.7

*1 These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: deg=expt<=105?4:expt<=210?5:6 or expt<=144?4:6; d=log10(c[deg])+deg*log10(m)[digits]; time=10^(d/30-4)[hours]; skew=|c0/c[deg]|^(1/deg); rlim=round(7*10^(d/60+3)); lpbr=floor(d/25+21); mfbr=floor(d/8+31); rlambda=floor(d/25+18)/10;

Efforts by ECM

The efforts by ECM to find small factors of this 226-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 40-digit or more. Please report your efforts by ECM. (Anonymous reports are not acceptable)

Level	B1	Reported runs Total / Required runs (Required runs for lower level)	Name
40	3e6	2111	Wataru Sakai	Feb 21, 2009
40	3e6	2111 / 2111
45	11e6	0 / 3974
45	11e6	/ 3974
50	43e6	0 / 7469 (1133)
50	43e6	/ 7469 (1133)
55	11e7	0 / 17752 (3098)
55	11e7	/ 17752 (3098)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

Command line to find prime factors up to about 45-digit

echo 8175148325906903122680185625669425023660537155932173967065765979014371672879372506633237742369517012811587639114220441728682304334212857047154742376051912609932907164545250372048695079876661938736569839930275314631428703255013 | ecm -n -c 3974 11e6

Command line to find prime factors up to about 50-digit

echo 8175148325906903122680185625669425023660537155932173967065765979014371672879372506633237742369517012811587639114220441728682304334212857047154742376051912609932907164545250372048695079876661938736569839930275314631428703255013 | ecm -n -c 7469 43e6

Command line to find prime factors up to about 55-digit

echo 8175148325906903122680185625669425023660537155932173967065765979014371672879372506633237742369517012811587639114220441728682304334212857047154742376051912609932907164545250372048695079876661938736569839930275314631428703255013 | ecm -n -c 17752 11e7

Command line to find prime factors up to about 60-digit

echo 8175148325906903122680185625669425023660537155932173967065765979014371672879372506633237742369517012811587639114220441728682304334212857047154742376051912609932907164545250372048695079876661938736569839930275314631428703255013 | ecm -n -c 42014 26e7

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